Convex Optimization of the Basic Reproduction Number

The basic reproduction number $R_{0}$ is a fundamental quantity in epidemiological modeling, reflecting the typical of secondary infections that arise from single infected individual. While widely known to scientists, policymakers, and general public, it has received comparatively little attention controls community. This note provides two novel characterizations : stability characterization geometric program characterization. allows us write -constrained budget-constrained optimal resource allocation problems as programs, which are easily transformed into convex optimization problems. We apply these programs allocating vaccines antidotes numerical examples, finding targeting instead spectral abscissa Jacobian matrix (a common target literature) leads qualitatively different solutions.